Jeff K., Sheila, Hang
Since the CHARD/DHARD noises are the dominant noise sources below 30 Hz, we tried to do a noise budget of their control outputs based on a freq-domain MIMO coherence analysis. The first two attached figures showed the noise budget of D/CHARD_P_OUT_DQ.
Conclusions:
1. We could explain well the ASC noise <= 3 Hz by using a combination of ISI residual motion, BOSEM sensing noise and L2A cross coupling from DARM actuation.
2. The ISI longitudinal residual motion dominates the total rms. It accounted for 83% (63%) of DHARD (CHARD) control output. Most of the rms is accumulated around 0.2 Hz due to the microseismic.
3. The DARM actuation L2A coupling matters only <0.2 Hz, and accounts for the rest of the DHARD rms.
4. The BOSEM sensing noise dominates from 0.5-3 Hz.
Possible solutions to reduce the ctrl output:
1. The local ISI-L to top mass L & P feeding forward should be the most effective way of reducing the control rms.
2. The M0 stage L2P decoupling on the actuation side can further reduce the DHARD rms < 0.2 Hz.
========================================================================================
Details:
We use a frequency domain MIMO coherence method to study the noise projection. This is a complementary method to the traditional way where we directly project each individual test mass's angular motion and add them incoherently (which might not be true for the seismic motion). In contrast, the MIMO coherence takes the correlation between different sensors' correlation into account by construction.
Q1. How much from actuation L2A cross-coupling?
While the seismic motion shakes all the test masses, we fed back the DARM signal only to ETMY during O2 (and CARM to MCL). Thus if the actuation cross-coupling matters, we should see an excess coherence between ETMY (whose motion is approximated by the oplev signals) and D/CHARD compared to the other test masses.
Therefore, we compare the coherence between ETMY and DHARD, and the coherence between ETMX and DHARD. The excess coherence is then attributed to actuation L2A.
As illustrated in the 3rd attachment, we only see a significant amount of extra coherence < 0.2 Hz. This indicates that the O2 coil balancing is sufficiently good and all we need to further optimize is the M0 stage L2A.
----
Q2. How much from residual seismic motion (i.e. ISI output)?
To answer this question, we compute the MISO coherence between 8 ISI channels (H1:ISI-*_SUSPOINT_*_EUL_L/P_DQ; * for EY/EX/IY/IX) and D/CHARD.
The resultant projection is shown in the 4th plot. It is dominated by the longitudinal motion (as expect) and dominates the total rms.
----
Q3. How much from BOSEM noise?
We compute the MISO coherence between 8 M0 damping channels (SUS-*_M0_DAMP_L/P_IN1_DQ) and D/CHARD. Those osem sensors should see both the residual seismic motion (as the ISI channels), and their own sensing noise ~ 2e-10 m/rtHz @ 1 Hz (the L2A actuation cross coupling will also be witnessed by those channels). Thus the excess coherence D/CHARD has with local damping channels relative to with the ISI channels are attributed to BOSEM noise.
The result is shown in the 5th plot. The excess < 0.2 Hz is actually due to actuation cross-coupling (cf. Q1) being witnessed by the osem sensors, while the noise in the 0.5-3 Hz is due to the true bosem sensing noise.
----
Q4. Do the noises add up to the total ASC noise?
Back to the 1st and 2nd plot. Once again, the BOSEM is actually a combination of actuation cross coupling (<0.2 Hz) and true BOSEM sensing noise. We separately show the actuation cross-coupling in dotted gray lines to emphasize its contribution but when adding the noise we do not include them to avoid double counting.
----
Q5. Where to find more plots and the analysis codes?
https://ldas-jobs.ligo.caltech.edu/~hang.yu/ASC/l2a/SEI_BOSEM/
For the ISI-L -> test mass pitch coupling, in addition to the local suspension channel, another possibility is that some seismic motion in the corner station causes angular noise in the recycling cavities, which further couples to CHARD/DHARD. The seismic motion is witnessed by the ITM ISI sensors and leads to the ISI-L to test mass pitch coherence.
If this is the case, we should see the ITM ISIs being more coherent with C/DHARD than the ETM ISIs.
We thus try to test this hypothesis and the result is shown in the 1st attached plot (we only show DHARD here, CHARD is similar). No excess coherence in ITM ISIs is found. In fact, the ETM ISIs' residual motion dominates the total DHARD-P noise.
This can be understood by examining the coherence between the ground motion at different points as shown in the second plot.
We see that the ground motions at ITMX and at ITMY are significantly correlated, while ITMX and ETMX are coherent only at the microseismic ~ 0.2 Hz. The ETMX and ETMY are mostly independent.
The coherence between ground motions indicates that when doing ASC noise budget, we could not simply add all the test masses' motions incoherently.
==============================================================================
We also perform a similar analysis for YAW.
We see an excess power from EY oplev (where DARM actuation goes) relative to EX oplev at microseismic, as shown in the 3rd plot. This suggests that we should do some actuation L2Y decoupling on the top mass (previously we only did pitch).
In the 4th plot, we see that the ISI residual motion (especially the longitudinal one) still is the largest contribution to the total DHARD-Y rms, and most of the contributions are from the ETMs. This suggests that the DHARD noise is mostly due to the seismic motion directly shaking the test masses. A large L2Y cross-coupling is not predicted in the Matlab suspension model, yet according to Jeff's measurement (LHO:42662) which reported an unexpectedly large L2L->L3Y coupling. it may be real... Would be nice to double check the ground L to test mass Y transfer function.
Lastly the bosem sensing noise contribution can be seen from the 5th plot.
In power, the actuation L2Y cross coupling and bosem sensing noise accounts for ~ 40% of DHARD-Y, while the rest seems to be from the residual seismic motion.